I am/was having almost exactly the same thing happen to me.
I formatted a newly purchased 1TB hard drive, as Mac OS Extended Journaled with encryption. When first using the hard drive i had absolutely no problems, i managed to backup my computer almost completely onto it without any hassles.
The hard drive then rested in a case for about a month, until i needed a file i no longer had on my mac, which was backed up in the hard drive. Though, at the time of creating the backup i tested the hard drive to make sure it was working, when i tried to access it a month later, it would cause the finder to crash in almost exactly the same manner described by the OP.
It would ask for my password, i would type it in, it would let me access the information for a couple of minutes at a time, and then hard drive would become unresponsive. Furthermore, finder would become catatonic.
I would try ejecting the hard drive to no avail (saying that the files were currently in use), i would try relaunching the finder (which would result in it not opening up again), i would try shutting the computer down (which would make it hang at the grey screen). I gave it time, hours in fact, but nothing would happen. At this point i would be forced to force a shut down using the power button.
I tried using Disk Utility to repair, or verify and i would always get an error indicating that the process encountered an error during the verify/repair process (no further details were given).
After trying for a very long time, and having my mac hang dozens of times, eventually i was able to access the information in the drive long enough to copy the files inside it to my hard drive and an older backup disk in which i cleared up some space. After doing this i reformatted the hard drive to simply Mac OS Extended Journaled and have been moving the information back into the drive.
I'm VERY suspicious of the drive however, i eliminated the encryption in case that was the problem, and in all reality i don't think in my case it was the actual problem. I was actually formatting it to return it, since i am still under warranty, but since it stopped being a hassle, it's probably a waste of time to try and get a replacement at this point

Besides, i am starting to think that its not a problem with the hardware per se, but maybe an incompatibility between the hardware and the encryption.
I am open to suggestions however.
Oh, and the drive draws power from USB... it has only one cable, no two headed USB port like other external hard drives i have.